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It is shown that for the generalized rigid body certain Cartan subalgebras (called of coordinate type) of so(n) are equilibrium points for the rigid body dynamics. In the case of so(4) there are three coordinate type Cartan subalgebras which on a regular adjoint orbit give three Weyl group orbits of equilibria. These coordinate type Cartan subalgebras are(More)
We prove that the study of stability using energy methods strongly depends on the conservation laws considered. We exemplify this by studying stability using Arnold's method in the case of so(4) free rigid body. Using the classical Mishchenko's constants of motion we do not obtain satisfactory stability results. We find new constants of motion generated by(More)
In 1936, the Romanian mathematician Dimitrie Pompeiu discovered the following simple, yet beautiful, result in Euclidean plane geometry [4], [5]: Pompeiu's Theorem. Let △ABC be an equilateral triangle, and let M be a point in the plane determined by it. Then, the lengths MA, MB, and MC form the sides of a triangle. The triangle formed by these sides is(More)
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